`g(t) = log_2(t^2+7)^3` Find the derivative of the function

`g(t) = log_2 (t^2+7)^3`

Before taking the derivative of the function, apply the logarithm rule `log_b (a^m)= m*log_b(a)` . So the function becomes:

`g(t) = 3log_2(t^2+7)`

Take note that the derivative formula of logarithm is `d/dx[log_b (u)] = 1/(ln(b)*u)*(du)/dx` .

So g'(t) will be:

`g'(t) = d/dt [3log_2 (t^2+7)]`

`g'(t) = 3d/dt [log_2 (t^2+7)]`

`g'(t) =3 * 1/(ln(2) * (t^2+7)) * d/dt(t^2+7)`

`g'(t) = 3 * 1/(ln(2) * (t^2+7)) * 2t`

`g'(t) = (3*2t)/(ln(2) * (t^2+7))`

`g'(t) = (6t)/((t^2+7)ln(2))`

Therefore, the derivative of the function is `g'(t) = (6t)/((t^2+7)ln(2))` .